I start my ski at home before I leave. I run it about 10 seconds and blip the throttle twice to make sure everything is working right.
I don't warm up my ski on the trailer. I don't run it out of the water at all unless I am doing something specific like starting it before the ride to check it and clearing the waterbox when we're done.
I always warm up my motor before I ride. I don't do this out of the water. I do this in the water. The 1st ride of the day I ride around for 1 min just off throttle, and 1 min half throttle. If it sits for more than 30 minutes, I'll cruise a lap or half lap on a long course before I really start reaming on it. If in doubt, stick your hand in the pisser, if it's not warm, your motor isn't warm.
Not an issue if you are going to cruise to your spot but if you are sitting on the beach next to the buoy course and are about to hold it WOT for an extended time, probably best to warm it up. Likely not an issue in the surf either because you are going to give it short burst of power, not just abuse it for 5 laps.